Question

A car is provided with 2 non overlapping wipers. The structure of each wiper is as shown in the figure. The brown blade actually wipes the glass sweeping through an angle of ${120}^{\circ }$. If the length of the wiper is 35 cm and the length of the blade is 28 cm, find the total area(in $c{m}^2$) cleaned for each sweep.

• A. 2500 $c{m}^2$
• B. 1800 $c{m}^2$
• C. 2464 $c{m}^2$
• D. 2000 $c{m}^2$

Answer 1

The correct option is C

2464 $c{m}^2$

As the wiper sweeps, area covered by each wiper is indicated in brown color below.

Area cleaned by each wiper = Area of sector AOB – Area of sector COD

Area of the sector of angle Ɵ = $\left(\frac{\theta }{{360}^{\circ }}\right)\times \pi \times r^2$

Area of sector AOB - Area of sector COD = $\frac{120}{360}\times \pi \times {35}^2-\left(\frac{120}{360}\right)\times \pi \times \left(7^2\right)$ =

= $\frac{120}{360}\times \pi \times ({35}^2-7^2)$

= 1232 $c{m}^2$

So, the total area cleaned by both the wipers = 2 × 1232 cm² = 2464 $c{m}^2$